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Optical systems: The eye, magnifier, microscope, telescope & binoculars . Hecht 5.7 Monday October 7, 2002. Human Eye, Relaxed. 20 mm. 15 mm. n’ = 1.33. F. H. H’. F’. 3.6 mm. P = 66.7 D. 7.2 mm. Accommodation. Refers to changes undergone by lens to enable imaging of closer objects

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optical systems the eye magnifier microscope telescope binoculars

Optical systems:The eye, magnifier, microscope, telescope & binoculars

Hecht 5.7

Monday October 7, 2002

human eye relaxed
Human Eye, Relaxed

20 mm

15 mm

n’ = 1.33

F

H

H’

F’

3.6 mm

P = 66.7 D

7.2 mm

accommodation
Accommodation
  • Refers to changes undergone by lens to enable imaging of closer objects
  • Power of lens must increase
  • There is a limit to such accommodation however and objects inside one’s “near point” cannot be imaged clearly
  • Near point of normal eye = 25 cm
  • Fully accommodated eye P = 70.7 for s = 25 cm, s’ = 2 cm
myopia near sightedness
Myopia: Near Sightedness

Eyeball too large ( or power of lens too large)

myopia near sightedness6
Myopia – Near Sightedness

Far point of the eye is much less than ∞, e.g. lf

Must move object closer to eye to obtain a clear image

Normal N.P.

Myopic

F.P.

Myopic

N.P.

myopia
Myopia

e.g. lf = 2m

How will the near point be affected?

0.5 + 66.7 = 67.2 D

is relaxed power of eye – too large!

To move far point to ∞, must decrease power to 66.7

Use negative lens with P = -0.5 D

laser eye surgery
Laser Eye surgery

Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball

Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue

Blurred

vision

Front view

laser eye surgery9
Laser Eye surgery

Radial Keratotomy – Introduce radial cuts to the cornea of the elongated, myopic eyeball

Usually use the 10.6 µm line of a CO2 laser for almost 100% absorption by the corneal tissue

Distinct

vision

Front view

Flattening

hyperopia far sightedness
Hyperopia – Far Sightedness

Eyeball too small – or lens of eye can’t fully accommodate

Image of close objects formed behind retina

hyperopia far sightedness11
Hyperopia – Far Sightedness

Suppose near point = 1m

Recall that for a near point of 25 cm, we need 70.7D

Use a positive lens with 3 D power to correct this person’s vision (e.g. to enable them to read)

Usually means they can no longer see distant objects - Need bifocals

correction lenses for myopia and hyperopia
Correction lenses for myopia and hyperopia

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/V/Vision.html

hand magnifier
Hand magnifier

Observation with unaided eye

θ

magnifier
Magnifier

To maximize the image, bring object as close to the eye as possible, i.e. bring object to near point s = ln = 25 cm

h’

θmax

hand magnifier15
Hand Magnifier

What is the angular magnification of the

image for an object at the near point or at ∞?

With thin lens

H,H’

h”

θ’

F

so

hM’

l

f

s’

L

compound microscope
Compound Microscope

x’

L

Fe

Fo

Fo

Fe

Recall xx’ = fo2

x

x’ ≈ L

Wish to have intermediate image (h’)

just inside the focus of the eyepiece

x = fo2/L

s’ ≈ fo + L

s = x + fo

compound microscope17
Compound Microscope

L

Fe

h

h’

Fo

Fo

Fe

h”

  • Recall: The magnification of an image formed
  • at the near point is
  • at infinity
compound microscope18
Compound microscope

Total magnification

(Image at infinity)

(Image at near point)

compound microscope19
Compound Microscope

In most microscopes, L ~ 16 - 17 cm

Objective

Eyepiece

(image at ∞)

10 X, 20 X, 40 X etc

fe = 2.5 cm

10X 

Me = 10

40X  fo = 0.4 cm

Overall magnification M = 40X10 = 400

compound microscope20
Compound Microscope

L

A.S.

Fe

Fo

Fo

Fe

EnP

ExP

Where should the eye be located to view the image?

  • Optimum viewing –
  • Place eye near ExP (moving eye away decreases illumination and F.O.V.)
  • Ensure that exit pupil ~ same size as eye pupil!
compound microscope21
Compound Microscope

L

A.S.

Fe

Fo

Fo

Fe

EnP

ExP

Chief Ray

Marginal ray

numerical aperture
Numerical Aperture

Measure of light gathering power

N. A. = n sin α

Lens

Air

Oil

αg

αg’

αo

αa

Cover Glass

ng

O

numerical aperture23
Numerical Aperture

If cover glass in air

If cover glass immersed in oil (no = 1.516) – between glass

and oil there is essentially no refraction since ng = 1.5

Increases the light gathering power by about 1.5

(N.A. roughly analogous to f# of a lens)

numerical aperture24
Numerical Aperture

In optical fibres

Cladding n2

Core n1

θc

θ

no

αmax

Cladding n2

N.A. = nosinαmax= n1sin θ = n1sin (90o - θc) = n1cos θc

This is a measure of the maximum cone of light accepted

viewing distant objects e g stars
Viewing distant objects, e.g. stars

star

h

θ

feye

Image size on retina h = feyeθ

telescope
Telescope

Objective

Eyepiece

fo

fe

hT=feyeθ’

θ’

θ

h’

θ’

h”

s’

telescope27
Telescope

Show

(magnification of the telescope)

(diameter of the exit pupil)

slide28

The Hubble Space Telescope

0.3 m secondary

mirror

2.4 m primary

mirror

binoculars
Binoculars

Two telescopes side-by-side

Prisms used to erect images

Objective

Eyepiece

binoculars30
Binoculars

“6 X 30”

Angular Magnification (M)

Diameter of objective lens, Do (mm)

Exit pupil = 5 mm, a good match to the normal pupil diameter

For night viewing, a rating of 7 X 50 is better: i.e. ~ 7 mm